Detecting and characterizing nanoscale material functionalities of emerging materials is of growing interest as it is critical for the advancement of nano- and bio-technology. Atomic force microscopy (AFM) is one technique for obtaining nano-scale information on functional materials and structures. Since AFM was developed as a topographical imaging technique, the capabilities of AFM-based techniques have been extended to include nano-scale mapping of various material characteristics such as electrical, material, chemical, electrochemical, and electromechanical properties over a broad range of materials, leading to advances in many fields including material science, physics, bio-mechanics, chemistry, and life sciences.
The traditional approach to AFM functional imaging involves the use of lock-in amplifiers to determine the amplitude and phase of the cantilever response at a single well-defined excitation frequency. The input to activate the material functionality can be in the form of a harmonic excitation applied to the base of the sample or directly to the tip, while the resulting cantilever deflections provide a measure of the functional properties of the sample. Depending on the functional response under investigation, the cantilever tip needs to remain in contact with the sample over the entirety of the oscillation cycle in a format known as Contact AFM (C-AFM) or over none of the oscillation cycle in a format known as Non-Contact AFM (NC-AMF). The C-AFM approach is the functional basis of AFM techniques such as Piezoresponse Force Microscopy (PFM), Electrochemical Strain Microscopy (ESM), and Infrared Spectroscopy (AFM-IR), in which the dimensional changes of a sample in response to the functional input are measured by the tip in contact. Similarly, NC-AFM is used in Electrostatic Force Microscopy (EFM), Kelvin Probe Force Microscopy (KPFM), and Magnetic Force Microscopy (MFM), in which the reacting force with respect to functional properties is measured by the non-contact tip.
The intrinsic limitation of many functional AFM techniques is the low Signal-to-Noise Ratio (SNR), especially when measuring materials of lower responsivity. One approach to improve the SNR is to increase the strength of the excitation. However, using a higher excitation input may be undesirable in many applications. For example, the high voltage input in PFM may cause polarization switching in ferroelectric materials or even damage to the sample. Alternatively, the SNR can be improved by utilizing resonance of the cantilever. By operating the cantilever near resonance, the cantilever response can be increased by a factor of 10˜100 (i.e., the Q factor of the cantilever resonance), thus significantly improving the SNR. Operating near resonance has proven beneficial in many AFM techniques such as single-frequency PFM, AFM-IR, KPFM, Atomic Force Acoustic Microscopy (AFAM) and MFM. However, in C-AFM methods that utilize contact resonance for signal amplification, the resonance frequency is primarily determined by the local tip-sample contact stiffness. Relying on the contact stiffness represents a major limitation of current contact-mode functional AFM techniques, because the contact stiffness varies due to topographic and material variations of the sample, consequently causing the resonant frequency to vary as well. Therefore, there can be significant crosstalk between sample topography and the functional response to the harmonic excitation, leading to undesirable artifacts and complicated interpretations of the functional properties. Moreover, in the absence of an invariant resonant frequency, calibration of the tip geometry and/or the force-sensor configuration can be extremely difficult, making quantitative measurements in AFM challenging to perform.
In order to overcome the limitations of the aforementioned techniques, recent efforts have been devoted to developing methods to track changes in the contact resonant frequencies of the cantilever as it scans over the surface. Resonant frequency tracking can be accomplished by adjusting the excitation frequency via a Phase Locked Loop (PLL). While PLLs have proven to be effective in techniques like NC-AFM and C-AFM (such as AFAM), they cannot be reliably used in cases where the relationship between the phase of the excitation and the driving signals strongly depends on local material properties. In other work, a Dual Frequency Resonance Tracking (DFRT) technique tracks the resonant frequency by measuring the amplitudes at two frequencies near resonance. In other work, a Band Excitation (BE) method excites and detects responses at all frequencies within a specified frequency range in the vicinity of the resonance. The commonality between DFRT and BE methods is that both techniques involve the excitation and detection of multiple frequencies to track changes in the contact resonant frequency, allowing the cantilever to be operated near resonance where PLLs are not possible. However, the main drawback of these methods is that they require additional data and signal processing, especially in the case of highly heterogeneous samples where BE requires a broader range of frequency inputs, whereas DFRT may fail to track any large scale resonant frequency changes.
What is needed, therefore, is a cantilever that provides a stable, i.e. invariant, contact resonant frequency, independent of changes in the local contact stiffness.